Two conductors have the same resistance at 0^ C but their temperature coefficients of resistance are ₁ and ₂ . The respective temperature coefficients of their series and parallel combinations are nearly

Step-by-step solution

Let R₀ be the initial resistance of both conductors At temperature their resistance will be, R₁=R₀ (1+ ₁ ) and R₂=R₀ (1+ ₂ ) for, series combination, R _ s = R ₁+ R ₂R_ s 0 (1+ _s )=R₀ (1+ ₁ )+R₀ (1+ ₂ ) where R _ s 0 = R ₀+ R ₀=2 R ₀ 2 R ₀ (1+ _s )=2 R ₀+ R ₀ ( ₁+ ₂ ) or _s= ₁+ ₂ 2 for parallel combination, R_p= R₁ R₂ R₁+R₂ where, R_ p 0 = R₀ R₀ R₀+R₀ = R₀ 2 R ₀ 2 (1+ _ p )= R ₀^2 (1+ ₁ + ₂ + ₁ ₂ ) R ₀ (2+ ₁ + ₂ ) as ₁ and ₂ are small quantities ₁ ₂ is negligible or _ p = ₁+ ₂ 2+ ( ₁+ ₂ ) = ₁+ ₂ 2 [1- ( ₁+ ₂ ) ] a